In triangle XYZ, ∠XYZ = 15 degrees, ∠XZY = 45 degrees and |XY| = 7 cm. Find |YZ|.

  • A 14√2 cm
  • B \(7\left(\frac{\sqrt{6}}{2}\right)\)
  • C 7√2 cm
  • D 7 cm
jamb 2006mathematics

The correct answer is B. \(7\left(\frac{\sqrt{6}}{2}\right)\)

∠yxz = 180 - (45 + 15)

= 180 - 60

= 120

Using sine rule

\(\frac{x}{sinx}=\frac{7}{sinz}\\

\frac{x}{sin 120}=\frac{7}{sin 45}\\

x=\frac{7 sin 120}{sin45}\\

x=\frac{7sin(180-120)}{sin 45}\\

x=\frac{7 sin 60}{sin 45}=\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\

x =\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\

x = 7\left(\frac{\sqrt{6}}{2}\right)\)

Previous question Next question